From Coherent Cosmic Oscillations to the Steady-State Cyclic Vibrating Universe Francis M. Sanchez1*, Valery A. Kotov2 1Universite Paris 11 (formerly), 20 Av. d'Ivry, 75013 Paris; e-mail: [email protected] 2Crimean Astrophysical Observatory, Nauchny, 98409 Crimea; e-mail: [email protected] Abstract. A Coherent Quantum Cosmology resolves the main cosmical enigma: Large Number correlations, dark matter, baryon density, vacuum energy. This is obtained from a non-reductionism analysis of data, and taking account of the Eddington's Fundamental theory and the non-Doppler cosmic oscillations with period tcc = 9600.606(12) s. The absence of Doppler effect (apart dephasages) induces the Tachyonic Principle: the world is divided in the c-visible part and a weakly interacting tachyonic one. In a gravitational Hydrogen Molecule, the Coherence Principle (identifying the ratio energy/h to an unifying frequency) gives the redshift (or Hubble) radius compatible with cT, where T ≈ 13.80(4) Gyr is the standard so-called Universe age. This model introduces an external Grandcosmos, considered as the source of the microwave background, the lacking element of the steady-state cosmology, and is tied to the vacuum energy, explaining its relative density about 10120. In the critical Universe, classical and quantum energies egalise, in a new application of the Coherence Principle, and the Eddington's Number 136 × 2256 of hydrogen atoms gives a baryon energy density related to the black matter one by b ≈ m²/2 ≈ 0.045. With teF 3 ≡ ħƛ e /GF the electron Fermi time, a c-free analysis defines a time 2tcc²/teF, again compatible with T, confirming this is not any age but a fundamental period (Cycling Principle). In a Galilean critical steady-state Universe, the Coherent Principle applies a third time with the kinetic and potential energies equalised with the Eddington's one. The corresponding density is 3/10, resolving an unsolvable mystery of mainstream cosmology: the black energy density, compatible with the density 7/10. This Eddington model is shown to corresponds to a gravitational deuterium atom. This triple concordance, confirmed by many (40 or so) other correlations giving our proposal for TU = RU/c, calls for an unification of the two major cosmologies; the Primordial Big Bang is then -103 toppled in favor of the Permanent (13.812 Gyr Cycling) Vibrating Universe (tU ≈ 0.838 10 s), with a predicted value 70.79 km s-1 Mpc-1 for the invariant recession constant, connected plausibly with a matter-antimatter scanned oscillation, resolving the antimatter and parity violation dilemma. Keywords: steady-state cosmology, Grandcosmos, Coherence Principle, Eddington's Fundamental Theory, Coherent Cosmic Oscillation, Resonance Principle, Holophysics Principle, Tachyonic vacuum energy, Dark Matter, Dark Energy, BEH boson. 1 1. Introduction. Non-reductionist analysis of data and new Cosmology 1.1. 'Immergence' versus Emergence Over several centuries, contrary to old tradition, a majority of scientists believed that the Small will explain the Large. So, cosmology is nowadays considered as the most complex scientific domain, with a final complete blockage of both cosmology and theoretical physics1,2. Also, the reductionist attitude has the consequence that the scientific domain is divided in separated disciplines, so that Chemistry and Biology seem to be distinct from physical basic principles by mysterious 'emergent' phenomena. We definitely show here that the concept of 'immergence' is far more efficient, with for instance, the presentation in this article of precise cosmic relations between triple point temperatures of basic molecules and the mammal temperature. This permits an inverse interpretation of the Anthropic Principle, putting an end to its monstrous application leading to such an aberration as the unobservable Multiverse3. The fact that the scientific community was forced to accept this scientific deviation confirms the above announced complete failure of the reductionist approach. By contrast, our Grandcosmos is directly observable via the Cosmic Microwave Background (CMB), and is a lacking decisive element to complete the steady-state theory4,5, based on the Perfect Cosmological Principle4, which is confirmed in the present article. 1.2. Correlated versus free parameters A central point is that the physical parameters are numbers which are not recognized by any mathematical domain. The mainstream interpretation is they are not mathematical constants, they would be given by chance in a Primordial Big Bang (PBB). But this supposes that nowadays mathematics is complete. The fact that differential equations were issued from a physical analysis (an historical dispute between Newton and Leibniz), and not the contrary, was long forgotten. So, the logical step is to look for relations between these thirty or so parameters, called 'free' by the mainstream interpretation. This task is much easier with large numbers than with small numbers. Indeed, relations between large numbers were observed from the beginning of modern cosmology, in particular from Weyl's conjecture6, followed by Dirac's large Number's hypothesis7, then Eddington's Fundamental Theory8. But many considered this as sterile numerology and preferred to resort to 'an order of magnitude explanation', characteristic of the Anthropic Principle9,10. But this approach is refuted now by the recent access of cosmology to precision: the so-called Universe age is estimated to 0.3%, from the recent (March 2013) Planck mission11. In fact a precise cosmical parameter was foreseen for years by the community: the non-Doppler Coherent Cosmic Oscillation (CCO) period, measured in the ppm range12. Altough theorists call for revolutionnary observations, they reject it when it is too revolutionary (a preliminary version of this article was rejected without explanation by the astro-ph ArXivs in November 2013). 1.2.1. The rehabilitation of Eddington's theory In a mainstream reductionist context, when Eddington8 claimed he has found the atomic number of the Universe, he was considered as a fool, and severely mocked. Contrary to Dirac, Eddington rejected the PBB concept of a definite Universe age. This article will rehabilitate completely the Eddington's Theory, showing, in particular, that it gives directly both the matter and the baryon densities. 1.2.2. A censored prediction now validated Half the Universe recession radius was obtained in the first 3 minutes of a first sabbatical year (September 1997), through a logical c-free formulation analysis, a more precise terminology than the misleading one: 'three-fold elementary dimensional analysis' (Sanchez 1998, rejected by the CRAS, Comptes Rendus à l'Académie des Sciences, but deposed in the closed archives of the 2 Academy, to be open publicly in near future). This draft contains the correct prediction, apart a 2 factor, of the so-called Universe age estimated now to 0.3 %, as recalled above. The censure continued even after the predicted galactic recession acceleration was observed. It was finally published in 2006 and confirmed in 2011 and 201313. New decisive advances are presented here. The case is so constrained that a Coherent Quantum Cosmology emerges naturally from the holistic physical analysis, inducing a number of Principles, summarized in the Conclusion. 1.2.3. The CCO period A decisive step was the reconnaissance that the CCO period tcc ≈ 9600.606(12) s was directly connected, again by a c-free analysis, with the weak Fermi Constant13. Thus the correlations between Large Numbers begin to reach the 10-4 imprecision of the Newton constant. There is therefore no more doubt that a totally new advance in physics is on stage. Moreover, precise relations, of holographic conservation type, ties the Universe and a Grandcosmos radii with the CCO length13. Such a non-Doppler phenomena is simply declared 'impossible' by current standard c-limited physics. But it took 3 seconds to tie very precisely its period, measured in the ppm range, with the Fermi constant. This CCO seems to introduce an absolute time, because of the invariance of the phase for each quasar12, over tenths of years: this introduces naturally a 'Tachyonic Principle', as will be explained in this article. Detailed analysis led in 2004 to a G-free precise relation with the muon-electron mass ratio, which permitted to predict correctly two more decimals in the Fermi constant, which was validated in 2012, as explained in this article. So the decimal more we predict in this article for the Newton gravitational constant (at 2 sigma from the tabulated value) must be taken seriously. 1.2.4. The CMB and CNB characteristics Apart CCO, the CMB properties gives the most precise cosmic parameters, in the 0.1 % range. We present here new decisive correlations, including the standard Cosmic Neutrino Background (CNB). So, the standard cosmology has something right, even without any PBB, but need drastic reinterpretation. The precision of these relations is such that the Primordial Big Bang (PBB) is refuted for years. Also, the cosmic application of the Anthropic Principle, - and its associated Multiverse concept- is refuted, since it is valid only in the order of magnitude range. 1.3. Vibration versus Primordial Inflationary Big Bang This article shows that several justified calculations of the redshift timescale enter this precision 0.3%, meaning it is constant, so this is not an age, rather the time constant of the exponential redshift law of the steady-state cosmology4,5, and the connection with the